Something like this should work:
Option Explicit

Sub ImportData()
'This macro is installed into the master workbook

Dim fPATH As String, fNAME As String, NR As Long
Dim wbDATA As Workbook, wsMASTER As Worksheet

Set wsMASTER = ThisWorkbook.Sheets("Sheet1")                'edit this to the name of the master sheet
NR = wsMASTER.Range("A" & Rows.Count).End(xlUp).Row + 1     'next empty row on the master sheet

fPATH = "\\c\folder\"                                       'path to all files
fNAME = Dir(fPATH & "*.xls*")                               'get the first filename from the folder

Do While Len(fNAME) > 0                                     'process one file at a time til no more filenames
    Set wbDATA = Workbooks.Open(fPATH * fNAME)              'open the found file
    With Range("13:15,30:32")
        .EntireRow.Hidden = False                           'unhide the rows
        .Copy wsMASTER.Range("A" & NR)                      'copy into master sheet to empty rows
    End With
    wsMASTER.Range("A" & NR).Resize(6).Value = Range("B4").Value    'add key value in column A

    wbDATA.Close False                                      'close the found file
    NR = wsMASTER.Range("A" & Rows.Count).End(xlUp).Row + 1 'next empty row on the master sheet
    fNAME = Dir                                             'get the next filename
Loop

End Sub